Finite Group Databasebeta

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C4×#16837529 #28587309

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16837529

Splittings

SylowC59 ⋊ C4×#446

Subgroups

subgroupG/H
centerC2×C42C22×D59
commutatorC22×C59C22×C42
FrattiniC22×C4C23×D59
FittingC4×C4⋊C8×C59C2
socle, prime radicalC23×C59C23×C4
cosocleC22×C4×C59C24
hypercenterC4×C4⋊C8D59
hypocenterC59C4×#446
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

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, 168188);