Finite Group Databasebeta

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C4×#14581837 #24920668

order10624
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#14581837

Splittings

FittingC2×C4×D4×C83 ⋊ C2
SylowC83 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C23×D83
commutatorC2×C83C24×C4
FrattiniC22C24×D83
FittingC2×C4×D4×C83C2
socle, cosocleC22×C83C25
prime radicalC2×#14581837C2
hypercenterC2×C4×D4D83
hypocenterC83C4×H(5,𝔽2)
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

1660 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1708 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35295795, #35295796, #35295802, …
maximal normal subgroup of#35295795, #35295796, #35295802, …
maximal quotient ofC4×#19128174, C4×#19128173, C4×#19128176, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 17715);