Finite Group Databasebeta

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C4⋊C4×C59⋊C16 #28504033

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×C59⋊C16

Splittings

SylowC59 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D59
commutatorC2×C59C2×C4×C16
FittingC8×C4⋊C4×C59C2
socle, prime radicalC23×C59C22×C8
cosocleC22×C8×C59C23
hypercenterC8×C4⋊C4D59
hypocenterC59C16×C4⋊C4
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

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, 84912);