Finite Group Databasebeta

C4×#16837166 #28493875

order15104
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#16837166

Splittings

SylowC59 ⋊ C4×#341

Subgroups

subgroupG/H
centerC2×C42C22⋊D59
commutatorC4×C59C43
FrattiniC23×C4C22×D59
FittingC2×C4×M16×C59C2
socleC23×C59C2×C4⋊C4
prime radicalC24×C59C2×Q8
cosocleC23×C4×C59C23
hypercenterC2×C4×M16D59
hypocenterC59C4×#341
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×M16

910 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, 74754);