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C2×C32×C7⋊D91 #37525673

order22932
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C7

Aliases

direct productC2×C32×C7⋊D91

Splittings

Fitting, socleC2×C32×C72×C13 ⋊ C2
derived, HallC72×C13 ⋊ C22×C32
HallC32×C72×C13 ⋊ C22
HallC32×C72 ⋊ C2×D13
HallC32×C13 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C32×D13
SylowC13 ⋊ C2×C32×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C32C7⋊D91
commutator, cosocle, hypocenterC72×C13C22×C32
FrattiniC1G
Fitting, socleC2×C32×C72×C13C2
LCSG ▷ C72×C13
UCSC1 ◁ C2×C32

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 11466

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

5760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1618);