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C23×C4⋊C4×D59 #29495242

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×C4⋊C4×D59

Splittings

FittingC23×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C24×C4⋊C4

Subgroups

subgroupG/H
centerC25C22×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
FittingC23×C4⋊C4×C59C2
socleC25×C59C23
prime radicalC25×D59C22
cosocleC22×C59C26
hypercenterC23×C4⋊C4D59
hypocenterC59C24×C4⋊C4
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C25 ◁ C23×C4⋊C4

19742 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, 1076121);