Finite Group Databasebeta

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C2×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3 #72213961

order2400
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3

Splittings

Fitting, socleC2×C52 ⋊ #41⋊C3
HallC2×(D5⋊AGL(1,𝔽5))⋊C2 ⋊ C3
SylowC52 ⋊ C2×#41⋊C3

Subgroups

subgroupG/H
center, hypercenterC2((D5⋊AGL(1,𝔽5))⋊C2)⋊C3
commutator, cosocle, hypocenter#6057C22×C3
FrattiniC1G
Fitting, socleC2×C52#41⋊C3
LCSG ▷ #6057
UCSC1 ◁ C2

125 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72210652, C2×#72210663, C22×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3, …
maximal normal subgroup ofC2×#72210663, C22×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3, C4×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3
maximal quotient ofC22×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3, C4×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.