Finite Group Databasebeta

C2×Q8×Dic59 #16837868

order3776
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic59

Splittings

SylowC59 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D59
commutatorC2×C59C23×C4
FrattiniC22C23×D59
FittingC22×Q8×C59C2
socle, prime radicalC23×C59C23
cosocleC22×C59C24
hypercenterC22×Q8D59
hypocenterC59C2×C4×Q8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 1015);