Finite Group Databasebeta

C2×Q8×C59⋊C16 #28742171

order15104
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×C59⋊C16

Splittings

SylowC59 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC2×C59C23×C16
FrattiniC2×C8C23×D59
FittingC2×C8×Q8×C59C2
socle, prime radicalC23×C59C22×C8
cosocleC2×C8×C59C24
hypercenterC2×C8×Q8D59
hypocenterC59C2×Q8×C16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323050);