Finite Group Databasebeta

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C4×#14579206 #23776605

order10112
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#14579206

Splittings

FittingC2×C4×D4×C79 ⋊ C2
SylowC79 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C23×D79
commutatorC2×C79C24×C4
FrattiniC22C24×D79
FittingC2×C4×D4×C79C2
socle, cosocleC22×C79C25
prime radicalC2×#14579206C2
hypercenterC2×C4×D4D79
hypocenterC79C4×H(5,𝔽2)
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

1660 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34179660, #34179661, #34179667, …
maximal normal subgroup of#34179660, #34179661, #34179667, …
maximal quotient ofC4×#19099036, C4×#19099035, C4×#19099038, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 17715);