Finite Group Databasebeta

D23×#367 #15675175

order2944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD23×#367

Splittings

FittingC23×#367 ⋊ C2
SylowC23 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D23
commutatorC8×C23C22×C4
FrattiniC2×C8C22×D23
FittingC23×#367C2
socleC22×C23C2×D8
prime radicalC22×D23D8
cosocleC2×C8×C23C23
hypercenter#367D23
hypocenterC23C2×#367
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6288);