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D5×C5⋊(D37⋊C3) #26012829

order11100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×C5⋊(D37⋊C3)
unambiguous semidirect product(C5×D5)⋊(D37⋊C3)
unambiguous semidirect product(D5×C37⋊C3)⋊D5
unambiguous semidirect product(D5×D185)⋊C3

Splittings

Fitting, socle, derived, HallC52×C37 ⋊ C22×C3
HallD5×D185 ⋊ C3
HallC52×C37⋊C3 ⋊ C22
HallC37⋊C3 ⋊ D52
SylowC37 ⋊ C3×D52
SylowC52 ⋊ C2×D37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C37C22×C3
LCSG ▷ C52×C37
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#3874⋊(D37⋊C3), D5×C5⋊(#66526⋊C2), C3×D5×C5⋊(D37⋊C3), …
maximal normal subgroup ofD5×C5⋊(#66526⋊C2), C3×D5×C5⋊(D37⋊C3)
maximal quotient ofD5×C5⋊(#66524⋊C2), C3×D5×C5⋊(D37⋊C3), D5×C3⋊(C5⋊(D37⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11100, 102);