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2−1+4×#1181 #16836474

order3712
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×#1181

Splittings

FittingC29×2−1+4 ⋊ C4
SylowC29 ⋊ C4×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2C24×#1181
commutator, socleC2×C29C24×C4
FittingC29×2−1+4C4
prime radical2−1+4×D29C2
cosocleC2×D29C25
hypercenter2−1+4#1181
hypocenterC29C4×2−1+4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ 2−1+4

1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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) = 464

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 21492);