Finite Group Databasebeta

#104×D151 #23752223

order9664
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#104×D151

Splittings

Fitting#104×C151 ⋊ C2
SylowC151 ⋊ C2×#104

Subgroups

subgroupG/H
centerC4D4×D151
commutatorC4×C151C22×C4
FrattiniC2×C4C22×D151
Fitting#104×C151C2
socleC2×C151C2×C22⋊C4
prime radical#41×D151C2
cosocleC2×C4×C151C23
hypercenter#104D151
hypocenterC151C2×#104
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#104×D151, #421×D151, #34077654, …
maximal normal subgroup ofC2×#104×D151, #421×D151, #34077654, …
maximal quotient ofD4⋊C8×D151, Q8⋊C8×D151, #34067489, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9664, 560);