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C4×#16837132 #28479289

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16837132

Splittings

SylowC59 ⋊ C4×Q8⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D59
commutatorC4×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC4×C4⋊C8×C59C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenterC4×C4⋊C8D59
hypocenterC59C4×Q8⋊C8
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C43 ◁ C4×C4⋊C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 60168);