Finite Group Databasebeta

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C2×C3×C5×C7⋊D77 #44568936

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C5×C7⋊D77

Splittings

Fitting, socleC2×C3×C5×C72×C11 ⋊ C2
derived, HallC72×C11 ⋊ C22×C3×C5
HallC3×C5×C72×C11 ⋊ C22
HallC5×C72×C11 ⋊ C22×C3
HallC3×C72×C11 ⋊ C22×C5
HallC3×C5×C72 ⋊ C2×D11
HallC5×C72 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×C3×C7⋊D7
SylowC72 ⋊ C2×C3×C5×D11
HallC3×C11 ⋊ C2×C5×C7⋊D7
SylowC11 ⋊ C2×C3×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C7⋊D77
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C72×C11
UCSC1 ◁ C2×C3×C5

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 16170

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

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

Conjugacy classes & character table

8130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 638);