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C2×C7×D885 #37613440

order24780
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D885
unambiguous semidirect product(C2×C3)⋊(C7×D295)
unambiguous semidirect product(C2×C5)⋊(C7×D177)
unambiguous semidirect product(C2×C59)⋊(C7×D15)

Splittings

Fitting, socleC2×C3×C5×C7×C59 ⋊ C2
derived, HallC3×C5×C59 ⋊ C22×C7
HallC3×C5×C7×C59 ⋊ C22
HallC5×C7×C59 ⋊ C2×D3
HallC3×C7×C59 ⋊ C2×D5
HallC7×C59 ⋊ C2×D15
HallC5×C59 ⋊ C2×D3×C7
HallC3×C59 ⋊ C2×C7×D5
HallC3×C5×C7 ⋊ C2×D59
SylowC59 ⋊ C2×C7×D15
HallC5×C7 ⋊ C2×D177
HallC3×C7 ⋊ C2×D295
HallC3×C5 ⋊ C2×C7×D59
SylowC5 ⋊ C2×C7×D177
SylowC3 ⋊ C2×C7×D295

Subgroups

subgroupG/H
center, hypercenterC2×C7D885
commutator, cosocle, hypocenterC3×C5×C59C22×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C59C2
LCSG ▷ C3×C5×C59
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 76
transitive degreeμt(G) = 12390

A minimal faithful permutation representation — 2 generators on 76 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(61,62)(63,64)(66,67)(68,69,70,71,72,73,74);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(60,61,63,64,62)(65,66,67)(75,76)

Conjugacy classes & character table

6216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 102);