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C4×#16837149 #28479640

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16837149

Splittings

SylowC59 ⋊ C4×#332

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC4×C4⋊C8×C59C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenterC4×C4⋊C8D59
hypocenterC59C4×#332
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 60519);