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C2×C7⋊(C7⋊(D31⋊C5)) #44477157

order30380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C7⋊(C7⋊(D31⋊C5))
unambiguous semidirect product(C2×C7)⋊(C7⋊(D31⋊C5))
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C7⋊D7)
unambiguous semidirect product(C2×C7⋊D217)⋊C5

Splittings

Fitting, socleC2×C72×C31 ⋊ C2×C5
derived, HallC72×C31 ⋊ C22×C5
HallC72×ΓL(1,𝔽32) ⋊ C22
HallC2×C7⋊D217 ⋊ C5
HallΓL(1,𝔽32) ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2C7⋊(C7⋊(D31⋊C5))
commutator, cosocle, hypocenterC72×C31C22×C5
FrattiniC1G
Fitting, socleC2×C72×C31C2×C5
LCSG ▷ C72×C31
UCSC1 ◁ C2

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 3038

A minimal faithful permutation representation — 3 generators on 47 points:

(4,5)(6,7)(8,9)(11,12)(13,14)(15,16)(18,22,23,34,21,19,20,27,28,25)(24,39,40,41,26,30,31,43,45,33)(29,46,38,44,32,36,37,47,35,42);(1,2)(10,11,13,15,16,14,12)(17,18,21,26,28,35,45,39,23,29,38,46,40,42,30,22,20,24,32,43,37,47,36,27,31,41,44,34,33,25,19);(3,4,6,8,9,7,5)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 66);