Finite Group Databasebeta

C2×Q8×Dic389 #38734565

order24896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic389

Splittings

SylowC389 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D389
commutatorC2×C389C23×C4
FrattiniC22C23×D389
FittingC22×Q8×C389C2
socle, prime radicalC23×C389C23
cosocleC22×C389C24
hypercenterC22×Q8D389
hypocenterC389C2×C4×Q8
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

3920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1015);