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C4×#4041 #10605487

order640
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#4041

Splittings

FittingC4×C5×C4⋊C4 ⋊ C2
SylowC5 ⋊ C4×#121

Subgroups

subgroupG/H
centerC22×C4C22×D5
commutatorC22×C5C23×C4
FrattiniC23C23×D5
FittingC4×C5×C4⋊C4C2
socle, cosocleC23×C5C24
prime radicalC2×#4041C2
hypercenterC4×C4⋊C4D5
hypocenterC5C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11993830, #11993835, #11993850, …
maximal normal subgroup of#11993830, #11993835, #11993850, …
maximal quotient ofC4×#64954, C4×#64959, C4×#65277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 7569);