Finite Group Databasebeta

C4×Q8×D59 #16837865

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

Aliases

direct productC4×Q8×D59

Splittings

FittingC4×Q8×C59 ⋊ C2
SylowC59 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC2×C4C22×D59
commutatorC2×C59C23×C4
FrattiniC22C23×D59
FittingC4×Q8×C59C2
socle, cosocleC22×C59C24
prime radicalC22×D59C23
hypercenterC4×Q8D59
hypocenterC59C2×C4×Q8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 1012);