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C2×C32×C11×D13 #19104253

order5148
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C11×D13

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2
derived, SylowC13 ⋊ C22×C32×C11
HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ C22×C32
HallC32×C13 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11D13
commutator, hypocenterC13C22×C32×C11
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C13
UCSC1 ◁ C2×C32×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×D13×C11⋊C5, C32×D5×C11×D13, C2×C32×C5×C11×D13, …
maximal normal subgroup ofC2×C32×D13×C11⋊C5, C2×C32×C5×C11×D13, C2×C32×C7×C11×D13
maximal quotient ofC32×D5×C11×D13, C2×C32×C5×C11×D13, C2×C32×C11×D65, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 129);