Finite Group Databasebeta

C2×Q8×C22⋊D23 #15686869

order2944
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×C22⋊D23

Splittings

FittingC23×Q8×C23 ⋊ C2
SylowC23 ⋊ C2×D4×Q8

Subgroups

subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC23×Q8×C23C2
socleC23×C23C24
prime radicalC22×C22⋊D23C22
hypercenterC23×Q8D23
hypocenterC23C2×D4×Q8
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C23×Q8

1568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17982);