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C2×C5×#11924777 #26046076

order11970
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#11924777

Splittings

derived, HallC7×C19 ⋊ C2×C5×C9
HallC2×C5×C7×C19 ⋊ C9
HallC5×C7×C19 ⋊ C2×C9
HallC2×C7×C19 ⋊ C5×C9
HallC2×C5×C19 ⋊ C7⋊C9
HallC5×C19 ⋊ C2×C7⋊C9
HallC2×C5×C7 ⋊ #4294
HallC2×C19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C2×#4294
SylowC19 ⋊ C2×C5×C7⋊C9
HallC2×C7 ⋊ C5×#4294
SylowC7 ⋊ C2×C5×#4294

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5#87705
commutator, hypocenterC7×C19C2×C5×C9
FrattiniC3C2×C5×#87705
Fitting, socle, prime radicalC2×C3×C5×C7×C19C3
cosocleC3×C7×C19C2×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×#11924777, C5×#18012091, C5×#18012095, …
maximal normal subgroup ofC4×C5×#11924777, C5×#18012091, C5×#18012095, …
maximal quotient ofC4×C5×#11924777, C22×C5×#11924777

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 5);