Finite Group Databasebeta

C22⋊Q8×Dic23 #15675933

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×Dic23

Splittings

SylowC23 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC2×C23×C22⋊Q8C2
socle, cosocleC23×C23C24
prime radicalC24×C23C23
hypercenterC2×C22⋊Q8D23
hypocenterC23C4×C22⋊Q8
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7046);