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C2×(C112⋊C3)⋊C25 #31827558

order18150
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×(C112⋊C3)⋊C25
unambiguous semidirect product(C2×C112⋊C3)⋊C25
unambiguous semidirect product(C2×#15690027)⋊C3

Splittings

derived, SylowC112 ⋊ C2×C3×C25
HallC2×#15690027 ⋊ C3
Hall#15690027 ⋊ C2×C3
HallC2×C112⋊C3 ⋊ C25
HallC112⋊C3 ⋊ C2×C25
HallC2×C112 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5(C112⋊C3)⋊C5
commutator, hypocenterC112C2×C3×C25
FrattiniC5C2×(C112⋊C3)⋊C5
Fitting, socleC2×C5×C112C3×C5
prime radicalC2×C5×C112⋊C3C5
cosocleC5×C112C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13089712⋊C25, ((C11⋊Dic11)⋊C3)⋊C25, C4×(C112⋊C3)⋊C25, …
maximal normal subgroup of#13089712⋊C25, ((C11⋊Dic11)⋊C3)⋊C25, C4×(C112⋊C3)⋊C25, …
maximal quotient ofC4×(C112⋊C3)⋊C25, C22×(C112⋊C3)⋊C25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 42);