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C32×C5×Dic185 #45686136

order33300
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×Dic185

Splittings

derivedC5×C37 ⋊ C32×C4×C5
HallC32×C52×C37 ⋊ C4
HallC52×C37 ⋊ C32×C4
HallC32×C37 ⋊ C5×Dic5
HallC32×C52 ⋊ Dic37
SylowC37 ⋊ C32×C5×Dic5
SylowC52 ⋊ C32×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D185
commutator, hypocenterC5×C37C32×C4×C5
FrattiniC2C32×C5×D185
Fitting, socle, prime radicalC2×C32×C52×C37C2
cosocleC2×C5×C37C2×C32×C5
LCSG ▷ C5×C37
UCSC1 ◁ C2×C32×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6660

Conjugacy classes & character table

8460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 409);