Finite Group Databasebeta

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C4×#14581783 #24910021

order10624
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#14581783

Splittings

SylowC83 ⋊ C4×#125

Subgroups

subgroupG/H
centerC22×C4C22×D83
commutatorC22×C83C23×C4
FrattiniC23C23×D83
FittingC4×C4⋊C4×C83C2
socle, prime radical, cosocleC23×C83C24
hypercenterC4×C4⋊C4D83
hypocenterC83C4×#125
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

484 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1696 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35304391, #35304393, #35304396, …
maximal normal subgroup of#35304391, #35304393, #35304396, …
maximal quotient ofC4×#19127588, C4×#19127584, C4×#19127600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 7068);