Finite Group Databasebeta

C4×C4⋊(C59⋊C16) #28503994

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

Aliases

direct productC4×C4⋊(C59⋊C16)

Splittings

SylowC59 ⋊ C4×C4⋊C16

Subgroups

subgroupG/H
centerC2×C4×C8C2×D59
commutatorC2×C59C2×C4×C16
FrattiniC22×C8C22×D59
FittingC42×C8×C59C2
socle, prime radicalC23×C59C22×C8
cosocleC22×C8×C59C23
hypercenterC42×C8D59
hypocenterC59C4×C4⋊C16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4×C8 ◁ C42×C8

438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84873);