Finite Group Databasebeta

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C2×C3×C5×C7⋊D91 #50304514

order38220
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C5×C7⋊D91

Splittings

Fitting, socleC2×C3×C5×C72×C13 ⋊ C2
derived, HallC72×C13 ⋊ C22×C3×C5
HallC3×C5×C72×C13 ⋊ C22
HallC5×C72×C13 ⋊ C22×C3
HallC3×C72×C13 ⋊ C22×C5
HallC3×C5×C72 ⋊ C2×D13
HallC5×C72 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×C3×C7⋊D7
SylowC72 ⋊ C2×C3×C5×D13
HallC3×C13 ⋊ C2×C5×C7⋊D7
SylowC13 ⋊ C2×C3×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C7⋊D91
commutator, cosocle, hypocenterC72×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C13C2
LCSG ▷ C72×C13
UCSC1 ◁ C2×C3×C5

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 19110

A minimal faithful permutation representation — 3 generators on 37 points:

(3,4,5)(6,7,8,9,10)(12,13)(14,15)(16,17)(19,20)(21,22)(23,24)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37);(1,2)(18,19,21,23,24,22,20)(25,26,28,30,32,34,36,37,35,33,31,29,27);(11,12,14,16,17,15,13)

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1200);