Finite Group Databasebeta

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C4×C22⋊C4×Dic59 #28509763

order15104
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C43

Aliases

direct productC4×C22⋊C4×Dic59

Splittings

SylowC59 ⋊ C42×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC2×C59C2×C43
FrattiniC24C23×D59
FittingC2×C4×C22⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C42×C22⋊C4
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

3342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 90642);