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C5×Dic3×C61⋊C5 #32912957

order18300
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×Dic3×C61⋊C5
unambiguous semidirect productC3⋊(C4×C5×C61⋊C5)
unambiguous semidirect product(Dic3×C61)⋊C52
unambiguous semidirect product(C5×Dic3×C61)⋊C5

Splittings

derived, HallC3×C61 ⋊ C4×C52
HallC3×C5×C61⋊C5 ⋊ C4
HallDic3×C61 ⋊ C52
SylowC61 ⋊ C52×Dic3
SylowC3 ⋊ C4×C5×C61⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×C61⋊C5
commutator, hypocenterC3×C61C4×C52
FrattiniC2C5×D3×C61⋊C5
Fitting, socleC2×C3×C5×C61C2×C5
prime radicalC2×C3×C5×C61⋊C5C2
cosocleC2×C3×C61C2×C52
LCSG ▷ C3×C61
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 80);