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C3×Dic665 #22547587

order7980
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic665

Splittings

derived, HallC5×C7×C19 ⋊ C3×C4
HallC3×C5×C7×C19 ⋊ C4
HallC3×C7×C19 ⋊ Dic5
HallC3×C5×C19 ⋊ Dic7
HallC7×C19 ⋊ C3×Dic5
HallC3×C5×C7 ⋊ Dic19
HallC5×C19 ⋊ C3×Dic7
HallC3×C19 ⋊ Dic35
HallC5×C7 ⋊ C3×Dic19
HallC3×C7 ⋊ Dic95
SylowC19 ⋊ C3×Dic35
HallC3×C5 ⋊ Dic133
SylowC7 ⋊ C3×Dic95
SylowC5 ⋊ C3×Dic133

Subgroups

subgroupG/H
center, hypercenterC2×C3D665
commutator, hypocenterC5×C7×C19C3×C4
FrattiniC2C3×D665
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2004 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×Dic665, #4294⋊Dic35, (C7⋊C9)⋊Dic95, …
maximal normal subgroup ofC9×Dic665, #4294⋊Dic35, (C7⋊C9)⋊Dic95, …
maximal quotient ofC9×Dic665, C3×Dic1995, C32×Dic665

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 12);