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C5×(C79⋊C3)⋊Dic7 #45684398

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

Aliases

direct productC5×(C79⋊C3)⋊Dic7
unambiguous semidirect product(C79⋊C3)⋊(C5×Dic7)

Splittings

derived, HallC7×C79 ⋊ C3×C4×C5
HallC5×Dic553 ⋊ C3
HallC5×C7×C79⋊C3 ⋊ C4
HallC5×C7×C79 ⋊ C3×C4
HallDic553 ⋊ C3×C5
HallC7×C79⋊C3 ⋊ C4×C5
HallC5×C79⋊C3 ⋊ Dic7
HallC5×C79 ⋊ C3×Dic7
HallC79⋊C3 ⋊ C5×Dic7
SylowC79 ⋊ C3×C5×Dic7
HallC5×C7 ⋊ (C79⋊C3)⋊C4
SylowC7 ⋊ C5×(C79⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5(C79⋊C3)⋊D7
commutator, hypocenterC7×C79C3×C4×C5
FrattiniC2C5×(C79⋊C3)⋊D7
Fitting, socleC2×C5×C7×C79C2×C3
prime radicalC2×C5×C7×C79⋊C3C2
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

1060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 29);