Finite Group Databasebeta

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C3×C11×C13×Dic7 #26046419

order12012
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C13×Dic7

Splittings

derived, SylowC7 ⋊ C3×C4×C11×C13
HallC3×C7×C11×C13 ⋊ C4
HallC7×C11×C13 ⋊ C3×C4
HallC3×C7×C13 ⋊ C4×C11
HallC3×C7×C11 ⋊ C4×C13
HallC7×C13 ⋊ C3×C4×C11
HallC7×C11 ⋊ C3×C4×C13
HallC3×C7 ⋊ C4×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C13D7
commutator, hypocenterC7C3×C4×C11×C13
FrattiniC2C3×C11×C13×D7
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2
cosocleC2×C7C2×C3×C11×C13
LCSG ▷ C7
UCSC1 ◁ C2×C3×C11×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C11×C13×Dic7, C11×Dic7×C13⋊C9, C11×C13×Dic7⋊C9, …
maximal normal subgroup ofC9×C11×C13×Dic7, C11×Dic7×C13⋊C9, C11×C13×Dic7⋊C9, …
maximal quotient ofC9×C11×C13×Dic7, C3×C11×C13×Dic21, C32×C11×C13×Dic7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 9);