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C2×C5×D5×C361 #49115472

order36100
automorphism?
homologyAbelianization (H1) = C22×C5×C361 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D5×C361
unambiguous semidirect productC5⋊(C22×C5×C361)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C361)

Splittings

FittingC2×C52×C361 ⋊ C2
derivedC5 ⋊ C22×C5×C361
HallC52×C361 ⋊ C22
SylowC52 ⋊ C22×C361

Subgroups

subgroupG/H
center, hypercenterC2×C5×C361D5
commutator, hypocenterC5C22×C5×C361
FrattiniC19C2×C5×D5×C19
FittingC2×C52×C361C2
socleC2×C52×C19C2×C19
prime radicalC2×C5×D5×C19C19
cosocleC5×C19C22×C5×C19
LCSG ▷ C5
UCSC1 ◁ C2×C5×C361

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7220

Conjugacy classes & character table

14440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36100, 33);