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C7×#17983787 #44479171

order30492
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3×C11

Aliases

direct productC7×#17983787

Splittings

Fitting, socle, HallC32×C7×C112 ⋊ C4
derived, HallC32×C112 ⋊ C4×C7
HallC7×C112 ⋊ #157
SylowC112 ⋊ C7×#157
HallC32×C7 ⋊ #92150
SylowC32 ⋊ C7×#92150

Subgroups

subgroupG/H
center, hypercenterC7#17983787
commutator, hypocenterC32×C112C4×C7
FrattiniC1G
Fitting, socleC32×C7×C112C4
prime radicalC7×C3⋊(C3⋊(C11⋊D11))C2
cosocleC3⋊(C3⋊(C11⋊D11))C2×C7
LCSG ▷ C32×C112
UCSC1 ◁ C7

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 462

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 394);