Finite Group Databasebeta

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C3×C13×C7⋊#1042 #41031925

order27300
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C7⋊#1042

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C4
derived, HallC52×C7 ⋊ C3×C4×C13
HallC52×C7×C13 ⋊ C3×C4
HallC3×C52×C13 ⋊ Dic7
HallC3×C52×C7 ⋊ C4×C13
HallC52×C13 ⋊ C3×Dic7
HallC3×C7×C13 ⋊ #1042
HallC7×C13 ⋊ C3×#1042
HallC3×C52 ⋊ C13×Dic7
SylowC52 ⋊ C3×C13×Dic7
HallC3×C7 ⋊ C13×#1042
SylowC7 ⋊ C3×C13×#1042

Subgroups

subgroupG/H
center, hypercenterC3×C13C7⋊#1042
commutator, hypocenterC52×C7C3×C4×C13
FrattiniC1G
Fitting, socleC3×C52×C7×C13C4
prime radicalC3×C5×C7×D5×C13C2
cosocleC5×C7×D5C2×C3×C13
LCSG ▷ C52×C7
UCSC1 ◁ C3×C13

104 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

2847 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 815);