Finite Group Databasebeta

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C13×#6099 #72259185

order2704
automorphism?
homologyAbelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#6099

Splittings

SylowC132 ⋊ M16

Subgroups

subgroupG/H
centerC4×C13C2×D13
commutatorC2×C13C2×C4×C13
FrattiniC4C2×C13×D13
FittingC2×C4×C132C2
socleC2×C132C2×C4
prime radicalC22×C132C4
cosocleC4×C13C22×C13
hypercenterC2×C4×C13D13
hypocenterC13C13×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C13 ◁ C2×C4×C13

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72259190, C13×#88186, #72259276, …
maximal normal subgroup of#72259190, C13×#88186, #72259276, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.