Finite Group Databasebeta

C2×Q8×Dic373 #37559888

order23872
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic373

Splittings

SylowC373 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D373
commutatorC2×C373C23×C4
FrattiniC22C23×D373
FittingC22×Q8×C373C2
socle, prime radicalC23×C373C23
cosocleC22×C373C24
hypercenterC22×Q8D373
hypocenterC373C2×C4×Q8
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23872

Conjugacy classes & character table

3760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 1015);