Finite Group Databasebeta

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2−1+4×#88324 #28330645

order13568
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×#88324

Splittings

SylowC53 ⋊ C8×2−1+4

Subgroups

subgroupG/H
center, FrattiniC22C24×#6157
commutatorC2×C53C24×C8
Fitting, prime radicalC2×2−1+4×C53C4
socleC22×C53C24×C4
cosocleC2×Dic53C25
hypercenterC2×2−1+4#6157
hypocenterC53C8×2−1+4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×2−1+4

2190 conjugacy classes of subgroups; only the 1372 normal subgroups are shown.

normal subgroups only

This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 1372 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) = 6784

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1116121);