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C2×H(5,𝔽2)×C5⋊D5 #72221011

order3200
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214×C5

Aliases

direct productC2×H(5,𝔽2)×C5⋊D5

Splittings

FittingC2×C52×H(5,𝔽2) ⋊ C2
SylowC52 ⋊ C22×H(5,𝔽2)

Subgroups

subgroupG/H
centerC22C24×C5⋊D5
commutator, cosocleC2×C52C26
FrattiniC2C25×C5⋊D5
FittingC2×C52×H(5,𝔽2)C2
socleC22×C52C25
hypercenterC2×H(5,𝔽2)C5⋊D5
hypocenterC52C22×H(5,𝔽2)
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

26240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×H(5,𝔽2)×#1043, C5⋊D5×#3498, C2×C5⋊D5×#453, …
maximal normal subgroup ofC2×H(5,𝔽2)×#1043, C5⋊D5×#3498, C2×C5⋊D5×#453, …
maximal quotient ofC5⋊D5×#3498, C5⋊D5×#3484

GAP

Past the SmallGroups library coverage — no SmallGroups id.