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C4⋊C4×#11745689 #28748005

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4⋊C4×#11745689

Splittings

FittingQ8×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C4⋊C4×#41

Subgroups

subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingQ8×C4⋊C4×C59C2
socle, cosocleC23×C59C25
prime radicalC22×#11745689C22
hypercenterQ8×C4⋊C4D59
hypocenterC59C4⋊C4×#41
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 328884);