Finite Group Databasebeta

C22⋊Q8×Dic113 #28393110

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×Dic113

Splittings

SylowC113 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
FittingC2×C22⋊Q8×C113C2
socle, cosocleC23×C113C24
prime radicalC24×C113C23
hypercenterC2×C22⋊Q8D113
hypocenterC113C4×C22⋊Q8
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 7046);