Finite Group Databasebeta

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C2×#13104791 #72221348

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13104791

Splittings

FittingC22×C52×D4 ⋊ C4
SylowC52 ⋊ C2×#386

Subgroups

subgroupG/H
centerC23C22×#1043
commutatorC22×C52C23×C4
FrattiniC22C23×#1043
FittingC22×C52×D4C4
socleC23×C52C22×C4
prime radicalC22×D4×C5⋊D5C2
cosocleC22×C5⋊D5C24
hypercenterC22×D4#1043
hypocenterC52C2×#386
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×D4

6304 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72223242, C2×#120×#1043, #72258374, …
maximal normal subgroup of#72223242, C2×#120×#1043, #72258374, …
maximal quotient ofC2×#72221209, C2×#72221214, #72258570

GAP

Past the SmallGroups library coverage — no SmallGroups id.