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C4×#87886 #13106148

order1600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#87886

Splittings

FittingC22×C4×C52 ⋊ C22
SylowC52 ⋊ C2×C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D52
commutatorC2×C52C23×C4
FrattiniC22C22×D52
FittingC22×C4×C52C22
socle, cosocleC22×C52C24
prime radicalC2×#87886C2
hypercenterC22×C4D52
hypocenterC52C2×C4×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4

1088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#11717375, #72221094, C4×#11717471, …
maximal normal subgroup ofC4×#11717375, #72221094, C4×#11717471, …
maximal quotient of#72220757, #72223419, AGL(1,𝔽5)×#87886

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 8500);