Finite Group Databasebeta

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2−1+4×#92420 #30626566

order15616
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×#92420

Splittings

SylowC61 ⋊ C8×2−1+4

Subgroups

subgroupG/H
center, FrattiniC22C24×#6923
commutatorC2×C61C24×C8
Fitting, prime radicalC2×2−1+4×C61C4
socleC22×C61C24×C4
cosocleC2×Dic61C25
hypercenterC2×2−1+4#6923
hypocenterC61C8×2−1+4
LCSG ▷ C2×C61 ▷ C61
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) = 7808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1116121);