Finite Group Databasebeta

C2×Q8×Dic311 #34092160

order19904
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic311

Splittings

SylowC311 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D311
commutatorC2×C311C23×C4
FrattiniC22C23×D311
FittingC22×Q8×C311C2
socle, prime radicalC23×C311C23
cosocleC22×C311C24
hypercenterC22×Q8D311
hypocenterC311C2×C4×Q8
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19904

Conjugacy classes & character table

3140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 1015);