Finite Group Databasebeta

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Cayley diagram

C22×#1181 #90816

order464
isoclinismisoclinic class of #1181
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×#1181
unambiguous semidirect productD29⋊(C2×C4)

Splittings

Fitting, socleC22×C29 ⋊ C4
derived, SylowC29 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22#1181
commutator, hypocenterC29C22×C4
FrattiniC1G
Fitting, socleC22×C29C4
prime radicalC22×D29C2
cosocleD29C23
LCSG ▷ C29
UCSC1 ◁ C22

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 116

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#1181)⋊C4, C2×C4×#1181, C2×C4⋊#1181, …
maximal normal subgroup of(C2×#1181)⋊C4, C2×C4×#1181, C2×C4⋊#1181, …
maximal quotient ofC2×D29⋊C8, C2×#90796, D29⋊M16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 49);