Finite Group Databasebeta

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C5×#10619178 #72223275

order3200
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C29

Aliases

direct productC5×#10619178

Splittings

FittingC2×C52×H(5,𝔽2) ⋊ C2
SylowC52 ⋊ #3585

Subgroups

subgroupG/H
centerC2×C5C23×C22⋊D5
commutator, cosocleC4×C5C25×C5
FrattiniC4C24×C5×D5
FittingC2×C52×H(5,𝔽2)C2
socleC2×C52C23×D4
hypercenterC2×C5×H(5,𝔽2)D5
hypocenterC5C5×#3585
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C5×#41 ◁ C2×C5×H(5,𝔽2)

3826 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223301
maximal normal subgroup of#72223301

GAP

Past the SmallGroups library coverage — no SmallGroups id.