Finite Group Databasebeta

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C4×#14581757 #24909812

order10624
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#14581757

Splittings

SylowC83 ⋊ C42×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D83
commutatorC2×C83C22×C42
FrattiniC23C23×D83
FittingC4×C4⋊C4×C83C2
socle, prime radical, cosocleC23×C83C24
hypercenterC4×C4⋊C4D83
hypocenterC83C42×Q8
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

684 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35295000, #35295010, #35295020, …
maximal normal subgroup of#35295000, #35295010, #35295020, …
maximal quotient ofC4×#19127552, C4×C4⋊C4×Dic83, #35325576, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 6859);