Finite Group Databasebeta

C22×#10625011 #15686509

order2944
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#10625011

Splittings

SylowC23 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23#67272
commutator, cosocleC8×C23C24
FrattiniC8C23×D23
FittingC22×Q16×C23C2
socle, prime radicalC23×C23D8
hypercenterC22×Q16D23
hypocenterC23C22×Q32
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17622);