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C4×#16837580 #28594574

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#16837580

Splittings

SylowC59 ⋊ C4×#455

Subgroups

subgroupG/H
centerC2×C4#14273696
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×H(5,𝔽2)×C59C2
socleC22×C59C2×#120
prime radicalC2×H(5,𝔽2)×C59C22
cosocleC22×C4×C59C24
hypercenterC4×H(5,𝔽2)D59
hypocenterC59C4×#455
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×H(5,𝔽2)

1442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 175453);