Finite Group Databasebeta

#20266050

order6464
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

FittingC4⋊C4×C101 ⋊ C4
SylowC101 ⋊ #340

Subgroups

subgroupG/H
centerC22C22⋊#87938
commutatorC4×C101C42
FrattiniC2×C4C2×#87938
FittingC4⋊C4×C101C4
socleC22×C101C22⋊C4
hypercenterC4⋊C4#87938
hypocenterC101#340
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

114 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

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

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,101|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^10,g^e=g^100

Conjugacy classes & character table

278 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#20266050, #27186817, #27186819, …
maximal normal subgroup ofC2×#20266050, #27186817, #27186819, …
maximal quotient of#27185961, #27185966, #27185968, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6464, 1422);