Finite Group Databasebeta

C16×#11745685 #28742206

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

Aliases

direct productC16×#11745685

Splittings

FittingC2×C4×C16×C59 ⋊ C2
SylowC59 ⋊ C16×#41

Subgroups

subgroupG/H
centerC4×C16C2×D59
commutatorC2×C59C23×C16
FrattiniC2×C8C23×D59
FittingC2×C4×C16×C59C2
socleC22×C59C23×C8
prime radicalC2×#11745685C8
cosocleC2×C8×C59C24
hypercenterC2×C4×C16D59
hypocenterC59C16×#41
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323085);