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D5×C5⋊(C11⋊D11) #27130994

order12100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C11

Aliases

direct productD5×C5⋊(C11⋊D11)
unambiguous semidirect product(C5×D5)⋊(C11⋊D11)
unambiguous semidirect product(D5×C11)⋊D55

Splittings

Fitting, socle, derived, HallC52×C112 ⋊ C22
SylowC112 ⋊ D52
SylowC52 ⋊ C2×C11⋊D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C112C22
LCSG ▷ C52×C112
UCSC1

336 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#3874⋊(C11⋊D11), D5×C5⋊((C11⋊D11)⋊C3), C3×D5×C5⋊(C11⋊D11), …
maximal normal subgroup ofD5×C5⋊((C11⋊D11)⋊C3), C3×D5×C5⋊(C11⋊D11)
maximal quotient ofC3×D5×C5⋊(C11⋊D11), D5×C3⋊(C5⋊(C11⋊D11)), D15×C5⋊(C11⋊D11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 273);