Finite Group Databasebeta

C4×#16837131 #28479282

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16837131

Splittings

FittingC42×C8×C59 ⋊ C2
SylowC59 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42D236
commutatorC4×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC42×C8×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenterC42×C8D59
hypocenterC59C4×D4⋊C8
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 60161);