Finite Group Databasebeta

D23×#1271 #19212138

order5888
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productD23×#1271

Splittings

FittingC23×#1271 ⋊ C2
SylowC23 ⋊ C2×#1271

Subgroups

subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23C2×#1271
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

714 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5888, 57500);