Finite Group Databasebeta

D8×Dic373 #37559505

order23872
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic373

Splittings

SylowC373 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D373
commutatorC4×C373C22×C4
FrattiniC2×C4C22×D373
Fitting, prime radicalC2×D8×C373C2
socleC22×C373C2×D4
cosocleC2×C4×C373C23
hypercenterC2×D8D373
hypocenterC373C4×D8
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11936

Conjugacy classes & character table

2632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 632);