Finite Group Databasebeta

C2×Q8×Dic467 #44470503

order29888
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic467

Splittings

SylowC467 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D467
commutatorC2×C467C23×C4
FrattiniC22C23×D467
FittingC22×Q8×C467C2
socle, prime radicalC23×C467C23
cosocleC22×C467C24
hypercenterC22×Q8D467
hypocenterC467C2×C4×Q8
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29888

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1015);