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C5×#20268898 #45684396

order33180
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#20268898

Splittings

derived, HallC7×C79 ⋊ C3×C4×C5
HallC5×Dic7×C79 ⋊ C3
HallC5×#13110305 ⋊ C4
HallC5×C7×C79 ⋊ C3×C4
HallDic7×C79 ⋊ C3×C5
Hall#13110305 ⋊ C4×C5
HallC5×C79 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×Dic7 ⋊ C79⋊C3
SylowC79 ⋊ C5×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C4×C79⋊C3
HallDic7 ⋊ C5×C79⋊C3
SylowC7 ⋊ C4×C5×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#15693302
commutator, hypocenterC7×C79C3×C4×C5
FrattiniC2C5×#15693302
Fitting, socleC2×C5×C7×C79C2×C3
prime radicalC2×C5×#13110305C2
cosocleC2×C7×C79C2×C3×C5
LCSG ▷ C7×C79
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11060

Conjugacy classes & character table

1370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 27);