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C4×C5×C251⋊C5 #38737218

order25100
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC4×C5×C251⋊C5
unambiguous semidirect product(C4×C251)⋊C52
unambiguous semidirect product(C4×C5×C251)⋊C5

Splittings

FittingC4×C5×C251 ⋊ C5
derived, SylowC251 ⋊ C4×C52
HallC4×C251 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC4×C5C251⋊C5
commutator, hypocenterC251C4×C52
FrattiniC2C2×C5×C251⋊C5
FittingC4×C5×C251C5
socleC2×C5×C251C2×C5
prime radicalC2×C5×C251⋊C5C2
cosocleC2×C251C2×C52
LCSG ▷ C251
UCSC1 ◁ C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5020

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25100, 22);