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2−1+4×#10596842 #34035048

order18688
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×#10596842

Splittings

Fitting2−1+4×C73 ⋊ C8
SylowC73 ⋊ C8×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2C24×#10596842
commutator, socleC2×C73C24×C8
Fitting2−1+4×C73C8
prime radical2−1+4×D73C4
cosocleC2×#64408C25
hypercenter2−1+4#10596842
hypocenterC73C8×2−1+4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ 2−1+4

2190 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

normal subgroups only

This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 1063 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) = 1168

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1118632);