Finite Group Databasebeta

C2×Q8×Dic379 #37565710

order24256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic379

Splittings

SylowC379 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D379
commutatorC2×C379C23×C4
FrattiniC22C23×D379
FittingC22×Q8×C379C2
socle, prime radicalC23×C379C23
cosocleC22×C379C24
hypercenterC22×Q8D379
hypocenterC379C2×C4×Q8
LCSG ▷ C2×C379 ▷ C379
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24256

Conjugacy classes & character table

3820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 1015);