Finite Group Databasebeta

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C2×#13107746 #72221024

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13107746

Splittings

FittingC22×C52×D4 ⋊ C4
SylowC52 ⋊ C2×#518

Subgroups

subgroupG/H
centerC22C23×#1043
commutatorC2×C52C24×C4
FrattiniC2C24×#1043
FittingC22×C52×D4C4
socleC22×C52C23×C4
prime radicalC22×D4×C5⋊D5C2
cosocleC2×C5⋊D5C25
hypercenterC22×D4#1043
hypocenterC52C2×#518
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×D4

7680 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×H(5,𝔽2)×#1043, #72221206, C2×#72221214, …
maximal normal subgroup ofC2×H(5,𝔽2)×#1043, #72221206, C2×#72221214, …
maximal quotient of#72221206, #72223249, #72258310, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.