Finite Group Databasebeta

← Prev (#90800) Next (#90802) →

Cayley diagram

C22⋊#1181 #90801

order464
isoclinismisoclinic class of #90796
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

unambiguous semidirect productC22⋊#1181
unambiguous semidirect product(C2×#1181)⋊C2

Splittings

FittingC22×C29 ⋊ C4
SylowC29 ⋊ C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC2C2×#1181
commutator, socleC2×C29C2×C4
FittingC22×C29C4
prime radicalC22×D29C2
cosocleC2×D29C22
hypercenterC22#1181
hypocenterC29C22⋊C4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 33 points:

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

Polycyclic presentation:

2^4,29|a^2=c,b^a=bd,e^a=e^12,e^c=e^28

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745215, #11745227, #11745345, …
maximal normal subgroup of#11745215, #11745227, #11745345, …
maximal quotient of#11745215, #11745219, #11745221, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 34);