Finite Group Databasebeta

C22×Q8×Dic113 #28403750

order14464
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×Dic113

Splittings

SylowC113 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC24C22×D113
commutatorC2×C113C24×C4
FrattiniC22C24×D113
FittingC23×Q8×C113C2
socle, prime radicalC24×C113C23
cosocleC22×C113C25
hypercenterC23×Q8D113
hypocenterC113C22×C4×Q8
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C24 ◁ C23×Q8

1664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 17686);