Finite Group Databasebeta

C2×Q8×Dic599 #50306356

order38336
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic599

Splittings

SylowC599 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D599
commutatorC2×C599C23×C4
FrattiniC22C23×D599
FittingC22×Q8×C599C2
socle, prime radicalC23×C599C23
cosocleC22×C599C24
hypercenterC22×Q8D599
hypocenterC599C2×C4×Q8
LCSG ▷ C2×C599 ▷ C599
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38336

Conjugacy classes & character table

6020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38336, 1015);