Finite Group Databasebeta

← Prev (#72246227) Next (#72246229) →

C4×#72209641 #72246228

order6144
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C27

Aliases

direct productC4×#72209641

Splittings

FittingC4×#62817 ⋊ D3
derived#11710730 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22×C4#87588
commutator, hypocenter#11710730C2×C4
Frattini, socleC23C2×#87588
FittingC4×#62817D3
prime radicalC2×#72209641C2
cosocleC2×#11710730C22
LCSG ▷ #11710730
UCSC1 ◁ C22×C4

40086 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 40086 conjugacy classes of subgroups — too many to draw. Only its 95 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) = 64

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#72215854, AGL(1,𝔽5)×#72209641, C4×#72209832
maximal normal subgroup ofC4×#72215854, C4×#72209832
maximal quotient ofAGL(1,𝔽5)×#72209641

GAP

Past the SmallGroups library coverage — no SmallGroups id.