Finite Group Databasebeta

C42×#11745671 #28587161

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#11745671

Splittings

FittingC42×Q8×C59 ⋊ C2
SylowC59 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42C22⋊D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC42×Q8×C59C2
socleC23×C59C22×D4
prime radicalC22×D236C23
cosocleC22×C4×C59C24
hypercenterC42×Q8D59
hypocenterC59C42×SD16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×Q8

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 168040);