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C2×(C241⋊C3)⋊C25 #49116156

order36150
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×(C241⋊C3)⋊C25
unambiguous semidirect product(C2×C241⋊C3)⋊C25
unambiguous semidirect product(C2×C241⋊C25)⋊C3

Splittings

derived, SylowC241 ⋊ C2×C3×C25
HallC2×C241⋊C25 ⋊ C3
HallC241⋊C25 ⋊ C2×C3
HallC2×C241⋊C3 ⋊ C25
HallC241⋊C3 ⋊ C2×C25
HallC2×C241 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5(C241⋊C3)⋊C5
commutator, hypocenterC241C2×C3×C25
FrattiniC5C2×(C241⋊C3)⋊C5
Fitting, socleC2×C5×C241C3×C5
prime radicalC2×C5×C241⋊C3C5
cosocleC5×C241C2×C3×C5
LCSG ▷ C241
UCSC1 ◁ C2×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12050

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36150, 4);